SECTION C — Short Answer Type Questions [3 Marks Each]
- 3 Marks Q26. If P(−1,y) and Q(5,7) lie on a circle with center C(2,−3), find the value of y and hence find the radius of the circle.
- 3 Marks Q27. Find the coordinates of the point which divides the line segment joining A(4,−3) and B(8,5) in the ratio 3:1 internally
- 3 Marks Q28. Prove that the line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram. (Using coordinate geometry verification)
- 3 Marks Q29. Find the area of the triangle whose vertices are (1,−1), (−4,6), and (−3,−5).
- 3 Marks Q30. Find the area of the quadrilateral ABCD whose vertices are A(−4,−2), B(−3,−5), C(3,−2), and D(2,3).
- 3 Marks Q31. For what value of k are the points (k,2k), (3k,3k), and (3,1) collinear?
- 3 Marks Q32. If A(−5,7), B(−4,−5), C(−1,−6), and D(4,5) are the vertices of a quadrilateral, find its area by dividing it into two triangles.
- 3 Marks Q33. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0,−1), (2,1), and (0,3). Find the ratio of this area to the area of the given triangle
- 3 Marks Q34. Show that the points (a,b+c), (b,c+a), and (c,a+b) are collinear.
- 3 Marks Q35. If the vertices of a triangle are (1,k), (4,−3), and (−9,7) and its area is 15 square units, find the values of k.
- 3 Marks Q36. Find the area of the triangle formed by the coordinate axes and the line represented by 2x−4y+8=0.
- 3 Marks Q37. Prove that the coordinates of the centroid of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3) are (3x1+x2+x3,3y1+y2+y3)
- 3 Marks Q38. Find the third vertex of a triangle if two of its vertices are (−1,4) and (5,2), and its centroid is (0,−3).
- 3 Marks Q39. If the points P(k−1,2k), Q(3k,5k+1), and R(k+7,7k+5) are collinear, find the value of k.
- 3 Marks Q40. Find the area of the triangle formed by the points (a,c+a), (a,c), and (a+b,c).
- 3 Marks Q41. Let A(4,2), B(6,5), and C(1,4) be the vertices of △ABC. Median AD meets BC at D. Find the coordinates of point D and verify that median AD divides △ABC into two triangles of equal areas.
- 3 Marks Q42. If the points A(2,3), B(4,k), and C(6,−3) are collinear, find the value of k.
- 3 Marks Q43. Find the coordinates of the center and the radius of the circle passing through the points (0,2), (3,−1), and (3,3)
- 3 Marks Q44. If A(−1,0), B(3,1), C(2,2), and D(−2,1) are the points of a quadrilateral, show that ABCD is a parallelogram but not a rectangle.
- 3 Marks Q45. Find the value of k for which the points (3,−2), (k,2), and (8,8) are collinear
- 3 Marks Q46. If P(x,y) is any point on the line segment joining the points A(a,0) and B(0,b), prove that ax+by=1
- 3 Marks Q47. Find the coordinates of the orthocenter or incentre application: If the vertices of a triangle are (0,0), (3,0), and (0,4), find the coordinates of its in-center.
- 3 Marks Q48. A line intersects the x-axis and y-axis at P and Q respectively. If (2,−5) is the mid-point of PQ, find the coordinates of P and Q and the equation of the line.
- 3 Marks Q49. Prove using distance formula that the diagonals of a rhombus bisect each other at right angles, given vertices A(1,2), B(4,2), C(5,5), and D(2,5).
- 3 Marks Q50. Find the ratio in which the line segment joining A(3,−3) and B(−2,7) is divided by the x-axis. Also, find the coordinates of the point of division.
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English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.
தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.
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